The enigmas of Alan Turing

Second World War code-breaker Alan Turing was a national hero and a mathematical genius. Teacher Kester Brewin considers how his inspiring yet tragic story could engage your students.

This month sees the centenary of the birth of one of the truly great figures of the 20th century, a man who, it could be argued, profoundly changed the course of human history not once, but twice.

And yet, because of both the nature of his work and the workings of his nature, he was for many decades nearly forgotten.

Even now, as people are beginning to appreciate more widely just how great his legacy is, the British government are resisting calls to have him pardoned for the supposedly shameful crime that led to him taking his own life just two weeks before his 42nd birthday.

Alan Mathison Turing was born on June 23, 1912, and showed a strong aptitude for mathematics from an early age. Reading about his early life it is clear that he was passionate about learning. Turing enjoyed tackling any problem that was in front of him, and was happy to simply “have a go” using whatever tools he had within his grasp.

Using this approach he was able to get to grips with topics that were far more advanced than those that his peers were working on, without having even studied the methods of calculus that would have normally been employed to tackle them (like Einstein’s theory of relativity, which he got to grips with aged 16).

His appointment as a Fellow at King’s College was even granted on the basis of an innovative proof of the “Central Limit Theorem”, which Turing did not even realise had been proven over a decade before using a different method.

None of this mattered to Turing, and his gung-ho approach to simply diving in to learning is something that all students should be inspired by. Indeed, next time there is a light dusting of snow and pupils excuse themselves from school because it would be too treacherous to travel, remind them that Turing, finding that his first day at senior school coincided with the General Strike of 1926, cycled more than 60 miles to make sure that he was there on time!

Ironically, it was at this school, just as he was so happy to be in an intellectually stimulating environment, that tragedy struck, changing the course of his work for ever. Turing grew very close to, and fell in love with, an older boy called Christopher Morcom. Morcom was in the year above, but they shared a passion for science and mathematics.

Morcom showed the young Turing how to make a crystal radio set, perhaps the first “machine” that set him on a road to creating some of the greatest machines of our time. Entering the 6th form, Morcom and Turing were able to share classes together, and Turing made a point of sitting next to him in every lesson. Yet, very suddenly in 1930, Christopher Morcom died of bovine tuberculosis.

As the letter he wrote to Morcom’s mother testifies, Turing was utterly devastated by this loss, and immediately gave up his religious beliefs to become a staunch atheist. This change in his outlook was more than just about religious observation. Having formerly believed in a “soul”, Turing now became convinced that the brain was bio-mechanical, and “consciousness” a bio-chemical process. Brains, he posited, were incredibly sophisticated, but they were material objects, and thus machines nonetheless.

This was important because, as Turing developed as a mathematician and explored the fundamentals of logic, he proposed that it would be possible to build a machine that could so closely mimic the workings of the brain that it would have to be deemed “intelligent”.

For us now, and for the digitally native students that we teach, this does not seem such an extraordinary idea. But for the world of the 1930s and 40s, this was a completely unimaginable concept. Machines were common of course, but, despite their interior complexity, were very simple: each machine was designed to do just one thing. Hole punches punched holes. Amplifiers amplified. Washing machines washed. “Computers” did exist, but they tended to be young and female: a computer was a person who fed data into a machine that did computations.

Turing left school to study at Cambridge. He read mathematics as an undergraduate, and it is important to note that this is the backbone of everything that he achieved. When students question the value of studying mathematics, and algebraic logic in particular, Turing is the perfect person to point them to because the ways that he was able to apply his mathematics were not only philosophically profound, but also materially important to the tools that every one of us use every day.

While in Cambridge he wrote a paper that revolutionised the idea of what a machine could be made to do. On Computable Numbers, with an Application to the Entscheidungsproblem effectively provided the theoretical basis for every modern computer ever built.

It showed through the concept of the “Universal Turing Machine” that a machine could be made to do not just one thing, but be capable of doing anything that could be written as an algorithm.

Again, it is hard to see now just how revolutionary an idea this was. But try this with your students: get them to imagine approaching one of the great inventors in history like Da Vinci, Thomas Edison or Alexander Bell, and asking them to come up with a machine that could make and receive telephone calls, take pictures, access a virtually limitless library of information, tell you if your train is late, perform complex calculations, show you a map of anywhere in the world, and allow you to throw small angry birds at arrangements of pigs.

They could doubtless conceive of machines to do each of these things, but Turing was the first to see that a single digital device could be made to do all of them. It was this ability to take his mathematical genius and apply it to a diverse range of problems that saw Turing recruited to the secret government code-breaking facility at Bletchley Park during the Second World War.

Well documented now, though a secret for decades afterwards, Turing not only helped crack the German’s ultra-sophisticated Enigma code, but designed and had built a machine that could search quickly through the millions of possible cipher combinations.

This allowed British military command to intercept and decode top secret German messages within hours, rather than weeks. Thus Turing’s work turned the war in the Allies’ favour, shortened the conflict by perhaps two years, and potentially saved millions of lives.

Unable to speak about his work, and unrecognised by anyone, Turing went on from the war to continue his work into mathematics and computing at the National Physical Laboratory, and then in Manchester, writing another ground-breaking paper which outlined the principles of a computer which had programs stored in memory.

Having changed the course of world history by helping defeat the march of Nazism, Turing now gave the world the blueprints for the digital age that would follow.

It was while working on early computers in Manchester in 1952 that Turing’s house was broken into. When the police came to investigate and ask him about his personal circumstances, he openly admitted that he was gay and that the man who had likely broken in had recently spent the night. As homosexual activity was illegal, Turing was arrested and charged with gross indecency.

In an ironic twist of fate, the man who had done so much to show that the brain was no more than a machine now suffered the indignity of having his sexual orientation treated as though it were a mechanical fault that could be “fixed”.

Desperate to avoid jail, Turing was forced to accept chemical castration – injections of oestrogen that were meant to change his desires. Herein lies the tragedy of the way Turing was treated by those he served so brilliantly: though able to break the Enigma code, he was part of a society that could not accept the enigma that Turing himself was. His love for another man was incomputable by the society that hosted him, and, machine-like, it demanded he be “cured”.

What the hormone treatment did do was leave Turing profoundly distressed. Fearful of being ostracised by his academic peers, and with his security clearance removed because of government fears over homosexuals being seduced by Russian spies, Turing became increasingly depressed. On June 7, 1954, Alan Mathison Turing injected an apple with cyanide, ate it, and pulled the plug on his own life. He was 41.

As a mathematician, inventor, innovative thinker and war hero Turing is one of the greatest Britons to have ever lived.

His work and life are ripe for use across the mathematics, ICT, history and citizenship curricula, yet what his legacy also deserves is what is tragically still lacking for many of the gay students we teach: a full and glad acceptance by everyone in Britain of who they are.

His pardon for these apparent “crimes” cannot come too soon and every student should be inspired to lobby Parliament for it after hearing the story of this man to whom – from their civil liberties to their SmartPhones – they owe so much.

Kester Brewin teaches mathematics in south London. His new book Mutiny! Why We Love Pirates and How They Can Save Us is out now.